Method For Setting Nonpositive Deflection, Maximum Meshable Tooth Profile In Flat Wave Gear Device

ABSTRACT

In a flat wave gear device, there is determined a rack-approximated movement locus Lc 1  of a flexible externally toothed gear with respect to an S-side rigid internally toothed gear accompanying rotation of a wave generator, ρ OPT  is a minimum value of the radius of curvature of the movement locus Lc 1 , and is determined from an evolute e of the movement locus Lc 1 . A convex arc having a radius ρ (ρ≦ρ OPT ) is used in a main part of a tooth profile of the flexible externally toothed gear. A parallel curve c that is set apart from a movement locus Lc 2  by the arc radius ρ is used on a main part of a tooth profile to be generated on the S-side rigid internally toothed gear. The movement locus Lc 2  accounts for the actual number of teeth, and is obtained from a center A of a convex arc of the flexible externally toothed gear being drawn with respect to the rigid internally toothed gear. In a flat wave gear device that is provided with a flexible externally toothed gear having a non-positive deflection (κ≦ 1 ) tooth profile, a tooth depth of the flexible externally toothed gear can be increased, whereby ratcheting torque is increased and meshing can occur continuously over an entire range of a movement locus; and a load capacity of the flat wave gear device is increased.

TECHNICAL FIELD

The present invention relates to a flat wave gear device, and inparticular relates to a method for setting a tooth profile providing afunction whereby teeth continuously mesh at a low reduction ratio andratcheting torque is increased.

BACKGROUND ART

From the original invention of the wave gear device by C. W. Musser(U.S. Pat. No. 2,906,143) up to the present, a variety of inventionshave been proposed by Musser and numerous other researchers, includingthe present inventor. A variety of inventions have been proposed inregard to the tooth profile alone. One such invention proposed by thepresent inventor is a method for designing a tooth profile that appliesthe technique of rack approximation to the meshing between teeth of arigid internally toothed gear and teeth of a flexible externally toothedgear, whereby addendum profiles of both gears enabling wide-range toothengaging therebetween is derived (JP 45-41171 B). An application hasalso been filed for an invention used to avoid tooth profileinterference generated by rack approximation (JP 7-167228 A).

There is known a flat wave gear device configured to have an annularflexible externally toothed gear disposed within two rigid internallytoothed gears arranged in parallel, and an elliptical wave generatormounted in the interior thereof (JP 2503027). A typical flat wave geardevice is shown in FIG. 6. In a Hat wave gear device 100, one rigidinternally toothed gear 102 has the same number of teeth as a flexibleexternally toothed gear 104, and another rigid internally toothed gear103 has 2n more teeth (n is a positive integer) than the flexibleexternally toothed gear 104. In the present specification, the rigidinternally toothed gear having a different number of teeth than theflexible externally toothed gear is referred to as the “S-side rigidinternally toothed gear,” and the rigid internally toothed gear havingthe same number of teeth as the flexible externally toothed gear isreferred to as the “D-side rigid internally toothed gear.”

When a wave generator 105 having an elliptical contour is caused torotate, counter-rotation occurs between the flexible externally toothedgear 104 and the S-side, rigid internally toothed gear 103, which havedifferent numbers of teeth. For example, by securing the S-side rigidinternally toothed gear 103 so as to prevent rotation, and supportingthe D-side rigid internally toothed gear on the other side in arotatable state, reduced-speed rotation will be outputted from theD-side rigid internally toothed gear 102.

In order to prevent an increase in flexural stress caused by ellipticaldeformation of the flexible externally toothed gear at low reductionratios (e.g., 60 or higher) in a flat wave gear device, the degree ofradial deflection κmn (κ being the flexing coefficient, and m being themodule of both gears) must be reduced to κmn (κ<1) from mn (κ=1), whichis the normal degree of deflection (value obtained by dividing the pitchdiameter of the flexible externally toothed gear by the reduction ratiowhen the rigid internally toothed gear is fixed). Since tooth depth isrelated to the degree of deflection, reducing the deflection leads to adecrease in the tooth depth, and in turn to a decrease in the ratchetingtorque.

In order to prevent ratcheting under high load torque, it is necessaryto increase tooth depth as much as possible, and the meshing region mustbe maximally enlarged in association therewith. However, tooth profilesthat prevent ratcheting, which is a phenomenon whereby tooth-jumpingoccurs under high load torque, have yet to be proposed for flat wavegear devices having a low reduction ratio of 60 or less, such that theproblem is addressed while continuous contact is maintained at highdegree.

DISCLOSURE OF THE INVENTION

An object of the present invention is to provide a flat wave gear deviceprovided with a flexible externally toothed gear having a tooth profilesuch that κ≦1 (referred to as the “non-positive deflection” flexingcoefficient), wherein the tooth depth of the flexible externally toothedgear is increased, thereby allowing ratcheting torque to be raised, andmeshing to occur continuously over the entire range of a movement locus.

In order to overcome the problems described above, the present inventionis a method for setting a tooth profile in a flat wave gear device thathas an S-side rigid internally toothed gear disposed in parallel in acoaxial state with a D-side rigid internally toothed gear, an annularflexible externally toothed gear disposed in a coaxial state within theS-side and the D-side rigid internally toothed gears, and a wavegenerator for causing a cross-section of the flexible externally toothedgear given perpendicularly with respect to an axis thereof to flexelliptically and the resulting shape to rotate, the number of teeth onthe D-side rigid internally toothed gear being the same as the number ofteeth on the flexible externally toothed gear, and the number of teethon the S-side rigid internally toothed gear having 2n more teeth (nbeing a positive integer) than the number of teeth on theflexible-externally toothed gear, wherein the method is characterized incomprising:

using both the flexible externally toothed gear and the S-sideinternally toothed gear as spur gears of module m;

setting κmn (κ≦1) and −κmn as a degree of radial flexing on,respectively, a major and minor axis of an elliptically shaped rimneutral line of the flexible externally toothed gear in thecross-section of the flexible externally toothed gear givenperpendicularly with respect to the axis;

determining a rack-approximated movement locus of the flexibleexternally toothed gear with respect to the S-side rigid internallytoothed gear accompanying rotation of the wave generator;

taking ρ_(OPT) as a minimum value of a radius of curvature of themovement locus; and

using a convex arc having a radius ρ (ρ≦ρ_(OPT)) on a main part of atooth profile of the flexible externally toothed gear.

The radius ρ of the convex arc of the flexible externally toothed gearis preferably a value within a range of up to 5% of the minimum valueρ_(OPT).

The movement locus can be determined using formula (1),

an evolute of the movement locus can be determined using formula (2),

and the radius of curvature ρ_(OPT) can be determined using formula (3)with θ=π in the formula (2).

$\begin{matrix}{{x = {0.5\; {{mn}\left( {\theta - {\kappa \; \sin \; \theta}} \right)}}}{y = {{- \kappa}\; {{mn}\left( {1 - {\cos \; \theta}} \right)}}}} & (1) \\{{x = {{mn}\begin{bmatrix}{{0.5\left( {\theta - {\kappa \; \sin \; \theta}} \right)} + \frac{2\left\{ {{0.25\left( {1 - {\kappa \; \cos \; \theta}} \right)^{2}} + {\kappa^{2}\sin^{2}\theta}} \right\}^{1.5}}{\kappa \left( {\kappa - {\cos \; \theta}} \right)}} \\{\cos \left\{ {\tan^{- 1}\frac{0.5\left( {1 - {\kappa \; \cos \; \theta}} \right)}{\kappa \; \sin \; \theta}} \right\}}\end{bmatrix}}}{y = {{mn}\begin{bmatrix}{{\kappa \; \cos \; \theta} - 1 + \frac{2\left\{ {{0.25\left( {1 - {\kappa \; \cos \; \theta}} \right)^{2}} + {\kappa^{2}\sin^{2}\theta}} \right\}^{1.5}}{\kappa \left( {\kappa - {\cos \; \theta}} \right)}} \\{\sin \left\{ {\tan^{- 1}\frac{0.5\left( {1 - {\kappa \; \cos \; \theta}} \right)}{\kappa \; \sin \; \theta}} \right\}}\end{bmatrix}}}} & (2) \\{\rho_{OPT} = \frac{0.25\; {{mn}\left( {1 + \kappa} \right)}^{2}}{\kappa}} & (3)\end{matrix}$

The present invention is further characterized in comprising:

determining a movement locus wherein a center of the convex arc of theflexible externally toothed gear is drawn with respect to the S-siderigid internally toothed gear, with consideration given to the actualnumber of teeth;

determining a parallel curve set apart from the movement locus by radiusρ; and

using the parallel curve in a main part of a tooth profile to begenerated on the S-side rigid internally toothed gear.

It is preferable to determine a movement locus obtained from a toothcrest of the tooth profile of the flexible externally toothed gear beingdrawn with respect to the S-side rigid internally toothed gear, withconsideration given to the actual number of teeth; and to have a maximumvalue of a tooth depth of the tooth profile to be generated on theS-side rigid internally toothed gear be a value up to the extrema of themovement locus.

According to the flat wave gear device of the present invention, thetooth profiles of the flexible externally toothed gear and the rigidinternally toothed gears are defined by the method described above.

EFFECT OF THE INVENTION

According to the present invention, in a flat wave gear device that isprovided with a flexible externally toothed gear having a non-positivedeflection (κ≦1) tooth profile, a tooth depth of the flexible externallytoothed gear is increased, whereby ratcheting torque is increased andmeshing can occur continuously over an entire range of a movement locus;and a load capacity of the flat wave gear device is increased. The loadcapability of a flat wave gear device can thereby be increased.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a descriptive diagram showing a flat wave gear device in acase where the tooth difference is 2 (n=1);

FIG. 2 is a diagram showing a curve that expresses a rack-approximatedmovement locus of a tooth profile of a flexible externally toothed gearwith respect to a rigid internally toothed gear;

FIG. 3 is a diagram showing an evolute of the curve in FIG. 2 thatillustrates the movement locus;

FIG. 4 is a descriptive diagram showing an example of a tooth profile ofa flexible externally toothed gear obtained according to the presentinvention;

FIG. 5 is a descriptive diagram showing meshing between an S-side rigidinternally toothed gear and a flexible externally toothed gear, and atooth profile formed on the S-side rigid internally toothed gear, in across-section of a flat wave gear device given perpendicularly withrespect to the axis; and

FIG. 6 shows a perspective view, an exploded perspective view, and asectional view of a flat wave gear device.

BEST MODE FOR CARRYING OUT THE INVENTION

A method will be described below with reference to the attached drawingsfor setting tooth profiles of a flexible externally toothed gear and arigid internally toothed gear having different numbers of teeth in aflat wave gear device in which the present invention is applied.

The flat wave gear device is the same as the generic model shown in FIG.6. The number of teeth on an S-side rigid internally toothed gear andthe number of teeth on a flexible externally toothed gear differ by 2n(n is a positive integer), and the total amplitude of a movement locusof the flexible externally toothed gear is 2κmn (the flexing coefficientκ being a value of one or less, and m being the module).

FIG. 1 is a descriptive diagram showing an S-side rigid internallytoothed gear 2, a flexible externally toothed gear 4, and a wavegenerator 5 in a flat wave gear device 1 in which the difference betweenthe number of teeth is 2 (n=1).

(Method for Determining Tooth Profile of Flexible Externally ToothedGear)

FIG. 2 is a diagram showing a movement locus used as a basis forselecting an arc radius used to define a tooth profile of a main part(portion that includes a tooth profile of an addendum) of the flexibleexternally toothed gear 4. In a cross-section of the flexible externallytoothed gear 4 given perpendicularly with respect to the axis, themovement locus Lc1 is a rack approximation of relative movement betweenthe teeth of the flexible externally toothed gear 4 and the teeth of therigid internally toothed gear 2 accompanying rotation of the wavegenerator 5. Specifically, the movement locus Lc1 is the movement locusof the flexible externally toothed gear 4 in a case where anapproximation of rack meshing is made, wherein the rigid internallytoothed gear and the flexible externally toothed gear have an infinitenumber of teeth. The movement locus Lc1 is obtained using formula (1)below.

x=0.5 mn(θ−κ sin θ)

y=−κmn(1−cos θ)   (1)

A general formula for determining an evolute of the movement locus Lc1is used to determine the evolute of the movement locus Lc1 (locus of thecenter of curvature at every point of the movement locus). An evolute eis expressed by formula (2) below. Formula (2) is being indicated forthe first time by the present inventor. An example of the evolute e isshown in FIG. 3.

$\begin{matrix}{{x = {{mn}\begin{bmatrix}{{0.5\left( {\theta - {\kappa \; \sin \; \theta}} \right)} + \frac{2\left\{ {{0.25\left( {1 - {\kappa \; \cos \; \theta}} \right)^{2}} + {\kappa^{2}\sin^{2}\theta}} \right\}^{1.5}}{\kappa \left( {\kappa - {\cos \; \theta}} \right)}} \\{\cos \left\{ {\tan^{- 1}\frac{0.5\left( {1 - {\kappa \; \cos \; \theta}} \right)}{\kappa \; \sin \; \theta}} \right\}}\end{bmatrix}}}{y = {{mn}\begin{bmatrix}{{\kappa \; \cos \; \theta} - 1 + \frac{2\left\{ {{0.25\left( {1 - {\kappa \; \cos \; \theta}} \right)^{2}} + {\kappa^{2}\sin^{2}\theta}} \right\}^{1.5}}{\kappa \left( {\kappa - {\cos \; \theta}} \right)}} \\{\sin \left\{ {\tan^{- 1}\frac{0.5\left( {1 - {\kappa \; \cos \; \theta}} \right)}{\kappa \; \sin \; \theta}} \right\}}\end{bmatrix}}}} & (2)\end{matrix}$

In order to set the tooth profile of the main part of the flexibleexternally toothed gear 4, first, the main part of the tooth profile ofthe flexible externally toothed gear 4 is given as a convex arc a havingradius ρ with point A as the center. To maximize the range over whichthe gears 2, 4 mesh, the meshing range may be extended to the extremarelating to the point corresponding to the lowest value on the locus Lc1of the flexible externally toothed gear 4 with respect to the S-siderigid internally toothed gear 2; i.e., the singularity of the evolute e.Specifically, the movement locus Lc1 between point A, where meshingbegins (θ=180°), to point B, where meshing is deepest (θ=0°) may beused.

AB in FIG. 3 shows this range. The maximum value ρ_(OPT) of the arcradius ρ of the flexible externally toothed gear 4 is determinedtherefrom by formula (3) below, using 0=ρ in formula (2) above.

$\begin{matrix}{\rho_{OPT} = \frac{0.25\; {{mn}\left( {1 + \kappa} \right)}^{2}}{\kappa}} & (3)\end{matrix}$

Described above was an analysis of teeth meshing using rackapproximation. The movement locus Lc1 obtained by rack approximation issomewhat different from a movement locus when the actual number of teethis considered, but rack approximation is sufficient to determine themaximum value ρ_(OPT).

As long as it is merely for the meshing range to be kept to the maximum,the arc radius ρ of the flexible externally toothed gear 4 may fulfillthe relation ρ≦ρ_(OPT). In such a case, it is necessary to consider thebalance between the arcuate tooth profile (convex arc a) of the flexibleexternally toothed gear 4 and the tooth profile to be generated on therigid internally toothed gear 2, and avoid too small a radius value forconsiderations related to wear of the arcuate tooth profile. Taking theabove points into account, the arc radius ρ of the flexible externallytoothed gear 4 is preferably a value within a range of up to 5% of theminimum value ρ_(OPT).

FIG. 4 is a descriptive diagram showing an example of a tooth profile ofa flexible externally toothed gear and a rigid internally toothed gear.A tooth profile b of a dedendum connected to the arcuate profile a ofthe flexible externally toothed gear 4 should be one that causes nointerference, and comprises, e.g., a straight line and a fillet curve.

(Method for Determining Tooth Profile of S-Side Rigid Internally ToothedGear)

The tooth profile of the S-side rigid internally toothed gear 2 is oneformed according to the movement locus over which the arcuate toothprofile a of the flexible externally toothed gear 4 is drawn withrespect to the rigid internally toothed gear 2, with the actual numberof teeth being taken into account. In order to increase the ratchetingtorque, the tooth depth must be made as large as possible. Therefore,the movement locus is preferably used to the maximum extent.

FIG. 3 is used as a reference to describe determining the movement locusLc2, wherein the arc center of the arcuate tooth profile a of theflexible externally toothed gear 4 is drawn with respect to the S-siderigid internally toothed gear 2, and consideration is given to theactual number of teeth. A parallel curve c set apart from the movementlocus Lc2 by the arc radius ρ is determined. The parallel curve c isused on a main part of a tooth profile to be generated on the S-siderigid internally toothed gear 2.

It is moreover preferable to determine a movement locus that accountsfor the actual number of teeth and is obtained from a tooth crest of thetooth profile of the flexible externally toothed gear 4 drawn withrespect to the rigid internally toothed gear 2; and to have a maximumvalue of a tooth depth of the tooth profile to be generated on theS-side rigid internally toothed gear 2 be a value up to the extrema ofthe movement locus.

(Example of Meshing Between Flexible Externally Toothed Gear and S-SideRigid Internally Toothed Gear)

FIG. 5 shows meshing between an S-side rigid internally toothed gear anda flexible externally toothed gear, and a tooth profile formed on theS-side rigid internally toothed gear, in a cross-section of a flat wavegear device given perpendicularly with respect to the axis. The drawingshows that in a case where the S-side rigid internally toothed gear andthe flexible externally toothed gear have a finite number of teeth;i.e., 102 and 100 respectively, optimizing the arc radius according torack approximation as practiced in the present invention will also beeffective in a case where the number of teeth is finite. In this case,an optimal value is used for the arc radius of the tooth profile of theflexible externally toothed gear.

1. A method for setting a tooth profile in a flat wave gear device thathas a D-side and an S-side rigid internally toothed gears disposed inparallel in a coaxial state with each other, an annular flexibleexternally toothed gear disposed in a coaxial state within the D-sideand the S-side rigid internally toothed gears, and a wave generator forcausing a cross-section of the flexible externally toothed gear givenperpendicularly with respect to an axis thereof to flex elliptically andthe resulting shape to rotate, the number of teeth on the D-side rigidinternally toothed gear being the same as the number of teeth on theflexible externally toothed gear, and the number of teeth on the S-siderigid internally toothed gear having 2n more teeth (n being a positiveinteger) than the number of teeth on the flexible externally toothedgear, wherein the method is comprising: using both the flexibleexternally toothed gear and the S-side rigid internally toothed gear asspur gears of module m; setting κmn (κ≦1) and −κmn as a degree of radialflexing on, respectively, a major and minor axis of an ellipticallyshaped rim neutral line of the flexible externally toothed gear (a linepassing through the center part along a thickness direction of a toothroot rim when the flexible externally toothed gear is deformed into anelliptical shape) in the cross-section of the flexible externallytoothed gear given perpendicularly with respect to the axis; determininga rack-approximated movement locus of the flexible externally toothedgear with respect to the S-side rigid internally toothed gearaccompanying rotation of the wave generator; taking ρ_(OPT) as a minimumvalue of a radius of curvature of the movement locus; and using a convexarc having a radius ρ (ρ≦ρ_(OPT)) on a main part of a tooth profile ofthe flexible externally toothed gear.
 2. The method for setting a toothprofile in a flat wave gear device according to claim 1, comprising:setting the radius ρ of the convex arc of the flexible externallytoothed gear to be a value within a range of up to 5% of the minimumvalue ρ_(OPT).
 3. The method for setting a tooth profile in a flat wavegear device according to claim 1, comprising: determining the movementlocus using formula (1); determining an evolute of the movement locususing formula (2); and determining the radius of curvature ρ_(OPT) usingformula (3), with θ=π n in formula (2). $\begin{matrix}{{x = {0.5\; {{mn}\left( {\theta - {\kappa \; \sin \; \theta}} \right)}}}{y = {{- \kappa}\; {{mn}\left( {1 - {\cos \; \theta}} \right)}}}} & (1) \\{{x = {{mn}\begin{bmatrix}{{0.5\left( {\theta - {\kappa \; \sin \; \theta}} \right)} + \frac{2\left\{ {{0.25\left( {1 - {\kappa \; \cos \; \theta}} \right)^{2}} + {\kappa^{2}\sin^{2}\theta}} \right\}^{1.5}}{\kappa \left( {\kappa - {\cos \; \theta}} \right)}} \\{\cos \left\{ {\tan^{- 1}\frac{0.5\left( {1 - {\kappa \; \cos \; \theta}} \right)}{\kappa \; \sin \; \theta}} \right\}}\end{bmatrix}}}{y = {{mn}\begin{bmatrix}{{\kappa \; \cos \; \theta} - 1 + \frac{2\left\{ {{0.25\left( {1 - {\kappa \; \cos \; \theta}} \right)^{2}} + {\kappa^{2}\sin^{2}\theta}} \right\}^{1.5}}{\kappa \left( {\kappa - {\cos \; \theta}} \right)}} \\{\sin \left\{ {\tan^{- 1}\frac{0.5\left( {1 - {\kappa \; \cos \; \theta}} \right)}{\kappa \; \sin \; \theta}} \right\}}\end{bmatrix}}}} & (2) \\{\rho_{OPT} = \frac{0.25\; {{mn}\left( {1 + \kappa} \right)}^{2}}{\kappa}} & (3)\end{matrix}$
 4. The method for setting a tooth profile in a flat wavegear device according to claims 1 comprising: determining a movementlocus wherein a center of the convex arc of the flexible externallytoothed gear is drawn with respect to the S-side rigid internallytoothed gear, with consideration given to the actual number of teeth;determining a parallel curve set apart from the movement locus by radiusρ; and using the parallel curve in a main part of a tooth profile to begenerated on the S-side rigid internally toothed gear.
 5. The method forsetting a tooth profile in a flat wave gear device according to claim 4,comprising: determining a movement locus wherein a tooth crest of thetooth profile of the flexible externally toothed gear is drawn withrespect to the S-side rigid internally toothed gear, with considerationgiven to the actual number of teeth; and making a maximum value of atooth depth of the tooth profile to be formed on the S-side rigidinternally toothed gear a value up to the extrema of the movement locus.6. A flat wave gear device, having a tooth profile set using the methodof claim
 1. 7. A flat wave gear device, having a tooth profile set usingthe method of claim
 2. 8. A flat wave gear device, having a toothprofile set using the method of claim
 3. 9. A flat wave gear device,having a tooth profile set using the method of claim
 4. 10. A flat wavegear device, having a tooth profile set using the method of claim 5.